For the past two and a half years, I've been commuting between my
home in California and the MathWorks main office outside Boston.
This week, I cut 2700 miles off that commute by moving to Massachusetts.
So, my business mailing address is now:

Cleve Moler
The MathWorks, Inc.
24 Prime Park Way
Natick, MA 01760

The telephone number for the MathWorks switchboard is: 508-653-1415.
(That's 508-65-pi). You can reach my office phone directly by
dialing 508-653-2452 and then keying in extension 325.

My e-mail address remains moler@mathworks.com.

Our family's new home is in Sherborn, which is just south of Natick and
Framingham and a few miles west of Wellesey. The mailing address is:
62 Russett Hill Road, Sherborn, MA 01770.

If you're in the Boston area, and would like to visit the MathWorks,
let me know -- we'd be happy to see you.

Spectral analysis is usually done with the aid of the Fourier transform, which
is based on ideas inherited from the time of Fourier and makes full use of the
mathematical theory of complex analysis which, to a large extent, developed in
the last century in response to the need to resolve tricky problems of
integration and convergence thrown up by exploration of Fourier's theorem. As
students, we become familiar with the algebraic manipulation of complex
quantities and equations such as V=ZI become second nature to us; it is true
that when we come to evaluate ZI four multiplies are involved. In the days of
slide rules this factor four was very noticeable and although it is less
noticeable today, still, somewhere deep inside your calculator, four
multiplies are performed whenever two complex numbers are multiplied together.

When numerical Fourier analysis is performed complex operations are required
because the Fourier spectrum of a real waveform is necessarily complex.
Conversely, when we invert the Fourier transform we must have an algorithm
that accepts complex input. Thus, in the first case (real data) a lot of
unnecessary operations are carried out on an imaginary part that is
zero-valued, while in the second case (complex input) a lot of output values
are computed which are zero (or should be, to the limits of machine
precision). These elementary observations tell us that there should be a way
of performing spectral analysis of real data that avoids the wastefulness of a
transform that must be prepared for complex input, whereas most of the time
either our data are real, or our output is real.

This transform is the Hartley transform; it represents a waveform with
N sample values by N transform values which are real (see "Assessing the
Hartley Transform," IEEE Trans ASSP, vol. 38, 2174-2176, Dec 1990 and
references provided). Of course the Hartley transform graph is not the same
as the Fourier transform graph, which means that some of our intuition is
lost. On the other hand when we graph Fourier transforms we do not always
plot both the real and imaginary parts, which are not particularly clear to
grasp and which in fact change drastically for the same waveform if one only
changes the choice of origin of time. Usually we graph the power spectrum,
which is real and does not call on us to visualize the full complex transform.
The Hartley power spectrum is the same as the Fourier power spectrum;
likewise the Hartley phase is the same as the Fourier phase (with a 45 degree
shift). Also it is easy to learn how to see the real and imaginary parts of
the Fourier transform, given the Hartley transform, if you really want them.
In summary, it seems that we will continue to retain the advantage that we get
from fluency in complex algebra by using Fourier transforms in theoretical
work but that when we talk to computers which prefer real numbers we will
shift to the Hartley transform. By computing with real numbers we gain a
factor of two in speed in the inner loops of the algorithms. This can be very
important in new programming; however, if you have canned code that runs it is
usually not advised to tamper with it.

Interesting questions have been raised about the physical significance of the
Hartley transform relative to the Fourier transform. After all, Lord Kelvin
told us that "Fourier's theorem is not only one of the most beautiful results
of modern analysis, but it may be said to furnish an indispensable instrument
in the treatment of nearly every recondite question in modern physics." If
you have the opportunity to think about the Hartley transform in advance you
might like to consider whether the Fourier transform is more fundamental
physically.

The organizers for the conference are pleased to inform you
that the DEADLINE for submitting contributed abstracts has
been EXTENDED to MARCH 20, 1992. For those of you who
have not yet submitted your 100-word abstract, send it
NOW -- by e-mail to: meetings@siam.org
by fax to: 215-386-7999
or call the SIAM office at 215-382-9800 if you have any
questions. SIAM encourages electronic submission of
abstracts. To help in formatting your submission, plain TeX
or LaTeX macros are available upon request.

Both lecturers are with the Mathematics and Computer Science
Division, Argonne National Laboratory, Argonne, Illinois

The course will cover four main problem areas. These are
nonlinear equations and nonlinear least squares,
unconstrained optimization, constrained optimization, and
global optimization.

Registration Fees: SIAM Non-
Member Member Student

Advance $120 $135 $55
On-Site 135 155 75

Preprints, coffee and lunch are included in the registration
fees. Attendees are advised to preregister for the short
course. On-site registration cannot be guaranteed. Preprints
of the lecture materials will be distributed upon check-in
at the SIAM registration desk.

The short course will precede the Fourth SIAM Conference on
Optimization which will be held on Monday through
Wednesday, May 11-13, 1992, Hyatt Regency Hotel, Chicago,
Illinois.

Signal processing is making increasingly sophisticated use of linear algebra
on both theoretical and algorithmic fronts. The purpose of this workshop is
to bring signal processing engineers, computer engineers, and applied linear
algebraists together for an exchange of problems, theories and techniques.
Particular emphasis will be given to exposing broader contexts of the signal
processing problems so that the impact of algorithms and hardware will be
better understood.

The workshop will explore five areas by having a sequence of talks devoted to
the underlying signal processing problem, the algorithmic and analytic
techniques and, finally, implementation issues for each area. The five areas
are:
1) updating SVD and eigendecompositions;
2) adaptive filtering;
3) structured matrix problems;
4) wavelets and multirate signal processing;
5) linear algebra architectures (parallel/vector and other high
performance machines/designs).

Most of the workshop talks will be held in Conference Hall 3-180 on the entry
floor of the Electrical Engineering/Computer Science Building. This building
is located on the corner of Washington Avenue and Union Street, a block from
the IMA Main Office. The conference hall is on the Ethernet and has a
projection system for display of computer output.

TENTATIVE SCHEDULE

Monday, April 6

Gene Golub, Stanford/IMA
The canonical correlations of matrix pairs and their numerical computation

The Research Institute for Advanced Computer Science (RIACS) at the
NASA Ames Research Center, located in the San Francisco Bay Area
adjacent to Silicon Valley, is inviting applications for visiting
research positions for graduate students for the summer of '92 and for
post-doctoral appointments of up to two years begining in the Fall of '92.

RIACS carries out a basic research program in the computational
sciences to support the needs of NASA Ames scientific missions.
Specific areas of interest are: algorithms and software for parallel
scientific computation with applications to computational fluid
dynamics, adaptive and composite mesh methods for solving partial
differential equations, the design and implementation of compilers and
tools for parallel computers, and the analysis of high performance
networks.

The computing environment at NASA Ames Research Center includes a
Connection Machine (CM-2), an Intel iPSC/860, a Cray Y-MP and a
Cray-2. High performance graphics workstations are also available.

Visitors to RIACS are expected to collaborate with NASA Ames scientists.
Additional opportunities for collaboration abound with the many local
research universities and institutions.

Applicants should send resumes and descriptions of research interests
with references to: